Introduction to Finance

Table-based Solution:
Equation 9.8 can be easily modifi ed to handle annuity due problems as follows:
PVAD
n
= PMT(PVIFA
r
,
n
)(1 + 
r
) (LE9.2)
where PVAD is the present value of an annuity due and the (1 + 
r
) factor eff ectively com-
pounds each payment by one more year to refl ect the fact that payments start at the beginning 
of each period. 
In the preceding problem, the annual payment is $1,000, the time period is three years, and 
the interest rate is 8 percent. Using equation LE9.2, the present value of this annuity due would be,
PVAD
3
= $1,000[(PVIFA
8%,3
)(1 + 0.08)]
= 
$1,000[(2.577)(1.08)]
= 
$1,000(2.783)
= 
$2,783
The PVIFA of 2.577 comes from Table 9.4 at the intersection of the 8 percent interest rate 
column and the year-three row. Present value annuity due problems also can be solved with 
computer software programs and fi nancial calculators. 

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250
C H A PT E R 9 Time Value of Money
If you have a fi nancial calculator, you can verify the present value of an annuity due result 
for the preceding three-year annuity problem. First, clear the calculator. Next, enter 1000 for 
TI calculators (or –1000 for HP calculators) and press the PMT key. Then enter 8 and press 
the %i key, and enter 3 and press the N key. Finally, instead of pressing the CPT key, press 
the DUE key followed by the PV key to fi nd the present value of an annuity due of 2783.26, 
which rounds to $2,783.
Financial Calculator Solution:
Inputs:
3 
8 
1000
N 
%i 
PMT
Press: DUE PV
Solution: 2783.26
Spreadsheet Solution:
The present value of an annuity due problem is solved by again using Excel’s
 
present value 
(PV) fi nancial function, but adjusting for when the cash fl ows occur, as follows:
= PV(Rate,Nper,Pmt,FV,Type)
= 
PV(.08,3,–1000,0,1)
= 
$2,783.26
Note that the “Type” value was given a “1” to indicate beginning of period cash fl ows. 
Recall that previously we used a “0” value in “Type” to refl ect cash fl ows occurring at the end 
of each time period.
Interest Rates and Time Requirements 
for Annuity Due Problems
Tables containing FVIFA and PVIFA factors are not readily available for annuity due prob-
lems. Thus, it is better to use a spreadsheet program or a fi nancial calculator when trying to 
fi nd the interest rate for an annuity due problem. Let’s assume that the future value of an annu-
ity due problem is $6,153, each payment is $1,000, and the time period is fi ve years. What is 
the interest rate on this problem? If you have a fi nancial calculator, enter FV = 6153, PMT = 
–1000, and N = 5. Press the DUE key and the %i key to fi nd an 
r
of 7 percent.